Fast dose algorithm for generation of dose coverage probability for robustness analysis of fractionated radiotherapy.

A fast algorithm is constructed to facilitate dose calculation for a large number of randomly sampled treatment scenarios, each representing a possible realisation of a full treatment with geometric, fraction specific displacements for an arbitrary number of fractions. The algorithm is applied to construct a dose volume coverage probability map (DVCM) based on dose calculated for several hundred treatment scenarios to enable the probabilistic evaluation of a treatment plan.For each treatment scenario, the algorithm calculates the total dose by perturbing a pre-calculated dose, separately for the primary and scatter dose components, for the nominal conditions. The ratio of the scenario specific accumulated fluence, and the average fluence for an infinite number of fractions is used to perturb the pre-calculated dose. Irregularities in the accumulated fluence may cause numerical instabilities in the ratio, which is mitigated by regularisation through convolution with a dose pencil kernel.Compared to full dose calculations the algorithm demonstrates a speedup factor of ~1000. The comparisons to full calculations show a 99% gamma index (2%/2 mm) pass rate for a single highly modulated beam in a virtual water phantom subject to setup errors during five fractions. The gamma comparison shows a 100% pass rate in a moving tumour irradiated by a single beam in a lung-like virtual phantom. DVCM iso-probability lines computed with the fast algorithm, and with full dose calculation for each of the fractions, for a hypo-fractionated prostate case treated with rotational arc therapy treatment were almost indistinguishable.